Invariant subspace perturbations related to defective eigenvalues of $Δ$-Hermitian and Hamiltonian matrices

Structured perturbation results for invariant subspaces of $Δ$-Hermitian and Hamiltonian matrices are provided. The invariant subspaces under consideration are associated with the eigenvalues perturbed from a single defective eigenvalue. The results show how the original eigenvectors and generalized eigenvectors are involved in composing such perturbed invariant subspaces and eigenvectors.

💡 Research Summary

The paper develops a comprehensive structured perturbation theory for invariant subspaces of Δ‑Hermitian and Hamiltonian matrices when a single defective eigenvalue is perturbed by a small structured matrix. The authors first recall results from general matrix perturbation theory (particularly those in